On selectivity properties of discrete-time linear networks

A definition of the quality factor
Q
and the resonant angle
\theta_{0}
for discrete-time networks is presented. The definitions are based on the bilinear transform. Using this transform, the selectivity properties for discrete-time networks, such as switched capacitor (SC) and digital filters, are consistent with analog networks. Expressions for
Q
and
\theta_{0}
in terms of polar coordinate parameters
r
and
\theta_{p}
for a complex-conjugate pole pair and
x_{1}
and
x_{2}
for real-axis poles are given as well as the inverse relations. Canonic expressions for generic forms of a biquadratic function are also given. Finally, an accurate method for measurement of the parameters in second-order SC-filters and digital filters implemented in software is described.